The ATDHFB formula is probably the most commonly used in applications to
fission, whether to compute spontaneous fission half lives or induced fission
fragment distributions. Although it is known to give the correct collective
mass at least in the case of translations, as applied in practical calculations
the ATDHFB theory does not enforce a complete decoupling between collective and
non-collective motion: doing so would not only require solving the ATDHFB
equation ()-() self-consistently rather
than on a precomputed potential energy surface, it would also face conceptual
problems caused by symmetry breaking; see discussion in Chapter 6 of
[1]}. The adiabatic self-consistent collective (ASCC) model
solves many of these difficulties [2]}, [3]}, [4]}
but has not been applied yet on realistic simulations of fission. Another
limitation of the ATDHFB framework is that it assumes that at each point
\(\mathbf {q}\) , the system is in its lowest energy state. Extensions of the
formalism to include thermal excitations and diabatic motion have been proposed
but not tested in practice [5]}.
